No 2 (2011)

We consider existence and uniqueness of solution for the inverse problem of determination of the unknown coefficient α(x) at the u(t,x) in nondivergent parabolic equation in a plane. The additional information is given by @op@prepare∫ 0Tu(t,x)χ(t)dt, with χ(t) being the weight function. It should be noted that the coefficients of the equation depend both on time as well as spatial variable. For the problem concerned we obtain conditions sufficient for the existence and the uniqueness of generalized solution. We adduce the examples of the inverse problems satisfying the conditions imposed.

The suffient conditions of restoration problems' solvability in a class of the Ito stochastic differential systems of the first order (with random disturbances from a class of Wiener processes and the diffusion degenerated with regard to a part of variables) with the given properties of a movement, when a control is included into the coefficient of drift, are obtained by separation method. The structure of the control parameter is defined, ensuring sufficient conditions of the given integral manifold's existence of constructed equations' set in nonlinear and linear Problem statements.

It is fnished the study of the necessary and sufficient conditions of validity for discrete inequalities of Hardy type with variable limits of summation in the sequence spaces started in the papers @cite KH and @cite KH2.

This paper presents a model of M competing telecommunication companies. The telecommunication networks of companies have different attributes which assumed fix and the consumers have idiosyncratic tastes for these attributes. The networks are mandated to interconnect and the access charges are determined by companies cooperatively. M telecommunication network companies are engaged in a price competition to attract consumers. Each consumer selects a network and determines the consumption of the telecommunication services. The regulation policy of the telecommunication market is studied for this model.

An algorithm of the continuous analogue of Newton method (CANM) is proposed for the solving of the boundary value problems of beam transport. The efficiency of CANM has been practically shown on a number of the problems of beam dynamics leading to the solving of ordinary differential and integral equations. The solving of the problem of determining the optimal (in sense of some criterions of quality) parameters Pi for charged particles transportation systems taking into account different nonlinear effects, is given. The results of the calculation of the consistent invisible straight section (insertion) of the accelerator obtained with the help of CANM are shown.

The paper demonstrates the comparison of some different algorithms for solving systems of ordinary differential equations with complex constant coefficients describing the evolution of monochromatic linearly polarized plane electromagnetic waves in a stratified medium.

In this paper motions of a heavy rigid body, of which point of support performs vertical harmonical vibrations of a high frequency and a small amplitude, are studied. Using an approximate autonomous system of differential equations of the motion, an analysis of existence, bifurcations and stability of relative equilibrium is carried out, for which the mass center and the point of support of the body don't lie at the same vertical. It is shown that all of these relative equilibria are unstable.

The problem of thin film dielectric spectroscopy at terahertz (THz) frequencies is under study in the paper. It has been stated that the technique employing surface plasmons (SP) excitation by the probing radiation on the metal substrate surface can be effectively used for solving the problem. To adopt the SP spectroscopy technique to the THz range we have developed a number of methods and devices making possible to determine the SP's complex refractive index depending on the film's optical properties. Some of the methods are based on interference of bulk and (or) surface waves, others - on the intensity measurements of the SP field. In addition the methods developed enable one to perform the measurements for one pulse duration of the radiation.

We have obtained an expression for the velocity of propagation of small perturbations (sound velocity) in the medium consisting of fluid vapour bubbles and metal particles. In addition, we have assumed that the system is in thermodynamical equilibrium, vapour bubbles and metal particles are distributed homogeneously, the metal is incompressible ( = 0), the bubble and particle sizes and the distance between them is much smaller than sound wave length.

The paper demonstrates the Hamiltonian nature of ordinary differential equations describing the evolution of monochromatic linearly polarized plane electromagnetic waves in a stratified medium. The possibility and necessity of using symplectic numerical methods for integrating the resulting system of Hamilton equations is established.